We will now work with a specific collection of examples of algebraic
schemes that can be used for cryptosystems--hyperelliptic curves. In
this case we can explicitly give a system of representatives for the
elements of the K-group, a mechanism for ``reducing'' any element to
one of these representing elements and also a bound for the size of
the group. We will see in the next section how such information about
a group can be used to make computations with the group efficient.